Finite Group Databasebeta

C22×#16837143 #28556567

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16837143

Splittings

SylowC59 ⋊ C22×#330

Subgroups

subgroupG/H
centerC24(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC22×#97×C59C2
socle, prime radicalC24×C59C22⋊C4
cosocleC42×C59C24
hypercenterC22×#97D59
hypocenterC59C22×#330
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

1158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 137446);