C₁₃×Dic₃₇ #14515315

order	1924
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₃×Dic₃₇

Splittings

derived, Sylow	C₃₇ ⋊ C₄×C₁₃
Hall	C₁₃×C₃₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₃₇
commutator, hypocenter	C₃₇	C₄×C₁₃
Frattini	C₂	C₁₃×D₃₇
Fitting, socle, prime radical	C₂×C₁₃×C₃₇	C₂
cosocle	C₂×C₃₇	C₂×C₁₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 1924

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);(14,16,15,17)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₁₃×Dic₃₇, C₁₃×Dic₂₅₉, C₁₃×#13050653, …
maximal normal subgroup of	C₇×C₁₃×Dic₃₇, C₁₁×C₁₃×Dic₃₇, Dic₃₇×C₁₆₉, …
maximal quotient of	C₇×C₁₃×Dic₃₇, C₁₃×Dic₂₅₉, C₁₃×#13050653, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1924, 2);

C13×Dic37 #14515315