Finite Group Databasebeta

C2×#21422665 #28556000

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21422665

Splittings

FittingC22×C22⋊C8×C59 ⋊ C2
SylowC59 ⋊ C2×#1519

Subgroups

subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC22×C22⋊C8×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC22×#14273701C2
cosocleC22×C4×C59C24
hypercenterC22×C22⋊C8D59
hypocenterC59C2×#1519
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

1866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 136879);