C₂×D₃₈₇ #13095421

order	1548
isoclinism	isoclinic class of D₃₈₇
automorphism	Aut(G) order 195048
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₇₇₄
direct product	C₂×D₃₈₇
unambiguous semidirect product	(C₂×C₉)⋊D₄₃
unambiguous semidirect product	(C₂×C₄₃)⋊D₉

Splittings

Fitting	C₂×C₉×C₄₃ ⋊ C₂
derived, Hall	C₉×C₄₃ ⋊ C₂²
Sylow	C₄₃ ⋊ C₂×D₉
Sylow	C₉ ⋊ C₂×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃₈₇
commutator, cosocle, hypocenter	C₉×C₄₃	C₂²
Frattini	C₃	C₂×D₁₂₉
Fitting	C₂×C₉×C₄₃	C₂
socle	C₂×C₃×C₄₃	D₃
LCS	G ▷ C₉×C₄₃
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 774

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54);(4,11)(5,10)(6,9)(7,8)(13,54)(14,53)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)

Conjugacy classes & character table

390 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₉⋊(D₄₃⋊C₇), D₇×D₃₈₇, C₂×C₇×D₃₈₇, …
maximal normal subgroup of	C₂×C₉⋊(D₄₃⋊C₇), C₂×C₇×D₃₈₇, C₂×C₁₁×D₃₈₇, …
maximal quotient of	D₇×D₃₈₇, C₂×C₇×D₃₈₇, C₂×D₂₇₀₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1548, 14);

C2×D387 #13095421