Finite Group Databasebeta

C2×#21425715 #28741377

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21425715

Splittings

FittingC2×C59×#349 ⋊ C2
SylowC59 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC22×C59C23×C8
FrattiniC2×C8C23×D59
FittingC2×C59×#349C2
socleC22×C59C2×C22⋊C8
prime radicalC22×#11745685C4
cosocleC2×C8×C59C24
hypercenterC2×#349D59
hypocenterC59C2×#2115
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322256);