Finite Group Databasebeta

← Prev (#13097589) Next (#13097591) →

C₄×C₇×C₁₉⋊C₃ #13097590

order	1596
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₇×C₁₉⋊C₃
unambiguous semidirect product	(C₄×C₁₉)⋊(C₃×C₇)

Splittings

Fitting, Hall	C₄×C₇×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₃×C₄×C₇
Hall	C₇×C₁₉ ⋊ C₃×C₄
Hall	C₄×C₁₉ ⋊ C₃×C₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₇	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃×C₄×C₇
Frattini	C₂	C₂×C₇×C₁₉⋊C₃
Fitting	C₄×C₇×C₁₉	C₃
socle	C₂×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₇×C₁₉⋊C₃	C₂
cosocle	C₂×C₁₉	C₂×C₃×C₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 532

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4)(5,6,7,8,9,10,11)(13,14,16)(15,18,19)(17,21,20)(22,26,24)(23,27,25)(28,30,29);(12,13,15,19,24,29,26,14,17,22,27,16,20,25,18,23,28,30,21)

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₇×#4296, C₄×#11924780, C₄×#11924781, …
maximal normal subgroup of	C₄×C₇×#4296, C₄×#11924780, C₄×#11924781, …
maximal quotient of	C₄×C₇×#4294, C₇×Dic₃×C₁₉⋊C₃, C₃×C₄×C₇×C₁₉⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 13);