C₃₇×Dic₁₃ #14515314

order	1924
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×Dic₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₇	D₁₃
commutator, hypocenter	C₁₃	C₄×C₃₇
Frattini	C₂	D₁₃×C₃₇
Fitting, socle, prime radical	C₂×C₁₃×C₃₇	C₂
cosocle	C₂×C₁₃	C₂×C₃₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃₇

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);(38,40,39,41)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₃₇×Dic₁₃, C₃₇×Dic₉₁, C₃₇×#90865, …
maximal normal subgroup of	C₇×C₃₇×Dic₁₃, C₁₁×C₃₇×Dic₁₃, C₁₃×C₃₇×Dic₁₃, …
maximal quotient of	C₇×C₃₇×Dic₁₃, C₃₇×Dic₉₁, C₃₇×#90865, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1924, 1);

C37×Dic13 #14515314