Finite Group Databasebeta

C2×#21422179 #28503547

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

Aliases

direct productC2×#21422179

Splittings

SylowC59 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC22×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC22×M32×C59C2
socleC23×C59C22⋊C8
prime radicalC24×C59C2×C8
cosocleC22×C8×C59C23
hypercenterC22×M32D59
hypocenterC59C2×#1377
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×M32

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84426);