Finite Group Databasebeta

C22×#16837192 #28741404

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16837192

Splittings

SylowC59 ⋊ C22×#352

Subgroups

subgroupG/H
centerC23#14273642
commutatorC23×C59C23×C4
FrattiniC2×D4C23×D59
FittingC22×#123×C59C2
socleC23×C59#99
prime radicalC23×D4×C59C22
cosocleC2×D4×C59C24
hypercenterC22×#123D59
hypocenterC59C22×#352
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C22×#123

1486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322283);