Finite Group Databasebeta

C22×#16837840 #29495183

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16837840

Splittings

FittingC22×M32×C59 ⋊ C2
SylowC59 ⋊ C22×#509

Subgroups

subgroupG/H
centerC23C2×D472
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC22×M32×C59C2
socleC23×C59C2×D8
hypercenterC22×M32D59
hypocenterC59C22×#509
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076062);