Finite Group Databasebeta

C2×#21425855 #28741672

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21425855

Splittings

SylowC59 ⋊ C2×#2151

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC22×C59C23×C8
FrattiniC2×C8C23×D59
FittingC2×C59×#405C2
socleC23×C59C22×C8
prime radicalC24×C59C2×C8
cosocleC2×C8×C59C24
hypercenterC2×#405D59
hypocenterC59C2×#2151
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×#405

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322551);