Finite Group Databasebeta

C2×#21432948 #29452817

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21432948

Splittings

SylowC59 ⋊ C2×#2948

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
Fitting, prime radicalC23×D8×C59C2
socleC23×C59C22×D4
cosocleC2×C4×C59C25
hypercenterC23×D8D59
hypocenterC59C2×#2948
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033696);