C₅×Dic₁₁₉ #14558657

order	2380
isoclinism	isoclinic class of D₁₁₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×Dic₁₁₉
unambiguous semidirect product	C₇⋊(C₅×Dic₁₇)

Splittings

derived, Hall	C₇×C₁₇ ⋊ C₄×C₅
Hall	C₅×C₇×C₁₇ ⋊ C₄
Hall	C₅×C₁₇ ⋊ Dic₇
Hall	C₅×C₇ ⋊ Dic₁₇
Sylow	C₁₇ ⋊ C₅×Dic₇
Sylow	C₇ ⋊ C₅×Dic₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₁₉
commutator, hypocenter	C₇×C₁₇	C₄×C₅
Frattini	C₂	C₅×D₁₁₉
Fitting, socle, prime radical	C₂×C₅×C₇×C₁₇	C₂
cosocle	C₂×C₇×C₁₇	C₂×C₅
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₂×C₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 2380

A minimal faithful permutation representation — 2 generators on 33 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);(6,8,7,9)(11,16)(12,15)(13,14)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₅×Dic₁₁₉, C₅²×Dic₁₁₉, C₅×Dic₅₉₅, …
maximal normal subgroup of	C₂₅×Dic₁₁₉, C₅²×Dic₁₁₉, C₅×C₇×Dic₁₁₉, …
maximal quotient of	C₂₅×Dic₁₁₉, C₅²×Dic₁₁₉, C₅×Dic₅₉₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2380, 4);

C5×Dic119 #14558657