Finite Group Databasebeta

C2×#21426036 #28742458

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21426036

Splittings

SylowC59 ⋊ C2×#2189

Subgroups

subgroupG/H
centerC23C2×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
Fitting, prime radicalC22×#135×C59C2
socleC23×C59C2×D8
hypercenterC22×#135D59
hypocenterC59C2×#2189
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#135

1146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323337);