Finite Group Databasebeta

C22×#16837131 #28555032

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#16837131

Splittings

FittingC22×C4×C8×C59 ⋊ C2
SylowC59 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4D236
commutatorC4×C59C23×C8
FrattiniC42C23×D59
FittingC22×C4×C8×C59C2
socleC24×C59C22⋊C4
prime radicalC23×D236C4
cosocleC42×C59C24
hypercenterC22×C4×C8D59
hypocenterC59C22×D4⋊C8
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 135911);