Finite Group Databasebeta

C2×#21433186 #29453639

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21433186

Splittings

SylowC59 ⋊ C2×#2984

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#432C2
socleC23×C59C23×C4
prime radicalC24×C59C22×C4
cosocleC2×C4×C59C25
hypercenterC2×#432D59
hypocenterC59C2×#2984
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#432

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1034518);