Finite Group Databasebeta

C22×#16837403 #29452223

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16837403

Splittings

SylowC59 ⋊ C22×#417

Subgroups

subgroupG/H
centerC24C2×C22⋊D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
Fitting, prime radicalC23×#41×C59C2
socleC24×C59C2×D4
cosocleC2×C4×C59C25
hypercenterC23×#41D59
hypocenterC59C22×#417
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×#41

5502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033102);