Finite Group Databasebeta

C2×#21421992 #28478913

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21421992

Splittings

SylowC59 ⋊ C2×#1301

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC2×C59×#431C2
socleC23×C59#95
prime radicalC24×C59C4⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#431D59
hypocenterC59C2×#1301
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 59792);