Finite Group Databasebeta

C22×#16837215 #28741640

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

Aliases

direct productC22×#16837215

Splittings

SylowC59 ⋊ C22×#361

Subgroups

subgroupG/H
centerC23#14273648
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
Fitting, prime radicalC23×D8×C59C2
socleC23×C59#102
cosocleC2×C8×C59C24
hypercenterC23×D8D59
hypocenterC59C22×#361
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C23×D8

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322519);