Finite Group Databasebeta

C22×#16837534 #29454981

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#16837534

Splittings

FittingC23×D8×C59 ⋊ C2
SylowC59 ⋊ C22×#447

Subgroups

subgroupG/H
centerC24D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC23×D8×C59C2
socleC24×C59C2×D4
hypercenterC23×D8D59
hypocenterC59C22×#447
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

7470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1035860);