Finite Group Databasebeta

C2×#21432972 #29452844

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

Aliases

direct productC2×#21432972

Splittings

SylowC59 ⋊ C2×#2951

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
Fitting, prime radicalC22×#135×C59C2
socleC23×C59C22×D4
cosocleC2×C4×C59C25
hypercenterC22×#135D59
hypocenterC59C2×#2951
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

2806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 1033723);