Finite Group Databasebeta

C2×#21422172 #28500282

order15104
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#21422172

Splittings

SylowC59 ⋊ C2×#1373

Subgroups

subgroupG/H
centerC2×C8D472
commutatorC8×C59C22×C8
FrattiniC4×C8C22×D59
FittingC2×C4×C16×C59C2
socleC22×C59#335
prime radicalC23×C59#108
cosocleC4×C8×C59C23
hypercenterC2×C4×C16D59
hypocenterC59C2×#1373
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4×C16

230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 81161);