C₂²×Dic₁₉ #64546

order	304
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂²×Dic₁₉

Splittings

derived, Sylow

C₁₉ ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	D₁₉
commutator, hypocenter	C₁₉	C₂²×C₄
Frattini	C₂	C₂²×D₁₉
Fitting, socle, prime radical	C₂³×C₁₉	C₂
cosocle	C₂×C₁₉	C₂³
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂³

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 27 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉⋊#95, #10597323, #10597324, …
maximal normal subgroup of	C₁₉⋊#95, #10597323, #10597324, …
maximal quotient of	C₂²×C₁₉⋊C₈, C₂×#64520, C₂×C₄×Dic₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(304, 35);

C22×Dic19 #64546

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂²×Dic₁₉ #64546