Finite Group Databasebeta

C2×#21425867 #28741699

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21425867

Splittings

FittingC2×C59×#365 ⋊ C2
SylowC59 ⋊ C2×#2155

Subgroups

subgroupG/H
centerC22#106×D59
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
FittingC2×C59×#365C2
socleC22×C59C2×#106
prime radicalC23×D59SD16
cosocleC2×C8×C59C24
hypercenterC2×#365D59
hypocenterC59C2×#2155
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322578);