Finite Group Databasebeta

C2×#21421925 #28478085

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C42

Aliases

direct productC2×#21421925

Splittings

SylowC59 ⋊ C2×#1274

Subgroups

subgroupG/H
centerC22×C4C4×Dic59
commutatorC4×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC2×C59×#376C2
socleC23×C59#95
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#376D59
hypocenterC59C2×#1274
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#376

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 58964);