Finite Group Databasebeta

C2×#21426319 #28743972

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

Aliases

direct productC2×#21426319

Splittings

SylowC59 ⋊ C2×#2240

Subgroups

subgroupG/H
centerC23C2×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
Fitting, prime radicalC2×C59×#493C2
socleC23×C59C2×D8
hypercenterC2×#493D59
hypocenterC59C2×#2240
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#493

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 324851);