Finite Group Databasebeta

C2×#21422162 #28500241

order15104
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422162

Splittings

SylowC59 ⋊ C2×#1368

Subgroups

subgroupG/H
centerC23#14273659
commutatorC8×C59C22×C8
FrattiniC4×C8C22×D59
FittingC2×C59×#346C2
socle, prime radicalC23×C59#106
cosocleC4×C8×C59C23
hypercenterC2×#346D59
hypocenterC59C2×#1368
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#346

254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 81120);