Finite Group Databasebeta

C2×#21421976 #28478674

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21421976

Splittings

SylowC59 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC24(C2×D59)⋊C4
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC22×C22⋊C8×C59C2
socleC24×C59C22⋊C4
prime radicalC25×C59D4
cosocleC23×C4×C59C23
hypercenterC22×C22⋊C8D59
hypocenterC59C2×#1294
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59553);