Finite Group Databasebeta

C2×#21422185 #28503558

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21422185

Splittings

SylowC59 ⋊ C2×#1379

Subgroups

subgroupG/H
centerC22×C8C22⋊D59
commutatorC4×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC2×C59×#405C2
socleC23×C59C22⋊C8
prime radicalC24×C59M16
cosocleC22×C8×C59C23
hypercenterC2×#405D59
hypocenterC59C2×#1379
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C2×#405

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84437);