Finite Group Databasebeta

C22×#16837643 #29455787

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

Aliases

direct productC22×#16837643

Splittings

SylowC59 ⋊ C22×#467

Subgroups

subgroupG/H
centerC24C2×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC24×C8×C59C2
socleC24×C59C2×D4
prime radicalC25×C59D4
hypercenterC24×C8D59
hypocenterC59C22×#467
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C24×C4 ◁ C24×C8

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036666);