Finite Group Databasebeta

C2×#21422111 #28498934

order15104
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422111

Splittings

SylowC59 ⋊ C2×#1349

Subgroups

subgroupG/H
centerC23#14273648
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
Fitting, prime radicalC2×C59×#466C2
socleC23×C59#102
cosocleC22×C8×C59C23
hypercenterC2×#466D59
hypocenterC59C2×#1349
LCSG ▷ C2×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 79813);