Finite Group Databasebeta

C2×#21421997 #28478976

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21421997

Splittings

SylowC59 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic59
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC2×C59×#423C2
socleC23×C59#95
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#423D59
hypocenterC59C2×#1303
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#423

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59855);