Finite Group Databasebeta

C22×#16837844 #29495188

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

Aliases

direct productC22×#16837844

Splittings

FittingC22×Q32×C59 ⋊ C2
SylowC59 ⋊ C22×#510

Subgroups

subgroupG/H
centerC23D8×D59
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC22×Q32×C59C2
socleC23×C59C2×D8
prime radicalC22×#14273750C2
hypercenterC22×Q32D59
hypocenterC59C22×#510
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076067);