C₂×D₂₇₅ #11764081

order	1100
isoclinism	isoclinic class of D₂₇₅
automorphism	Aut(G) order 110000
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₅₅₀
direct product	C₂×D₂₇₅
unambiguous semidirect product	(C₂×C₁₁)⋊D₂₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₁₁

Splittings

Fitting	C₂×C₁₁×C₂₅ ⋊ C₂
derived, Hall	C₁₁×C₂₅ ⋊ C₂²
Sylow	C₂₅ ⋊ C₂×D₁₁
Sylow	C₁₁ ⋊ C₂×D₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₂₇₅
commutator, cosocle, hypocenter	C₁₁×C₂₅	C₂²
Frattini	C₅	C₂×D₅₅
Fitting	C₂×C₁₁×C₂₅	C₂
socle	C₂×C₅×C₁₁	D₅
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 550

A minimal faithful permutation representation — 2 generators on 38 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);(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(29,38)(30,37)(31,36)(32,35)(33,34)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×D₂₇₅, C₂×C₃×D₂₇₅, C₂×D₈₂₅, …
maximal normal subgroup of	C₂×C₃×D₂₇₅, C₂×C₁₁×D₂₇₅, C₂×C₁₃×D₂₇₅, …
maximal quotient of	D₃×D₂₇₅, C₂×C₃×D₂₇₅, C₂×D₈₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1100, 14);

C2×D275 #11764081