Finite Group Databasebeta

C22×#16837426 #29452301

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16837426

Splittings

SylowC59 ⋊ C22×#423

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC23×C42×C59C2
socleC24×C59C22×C4
prime radicalC25×C59C2×C4
cosocleC2×C4×C59C25
hypercenterC23×C42D59
hypocenterC59C22×#423
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C23×C42

3438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033180);