Finite Group Databasebeta

C23×Dic472 #29495171

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic472

Splittings

SylowC59 ⋊ C23×Q32

Subgroups

subgroupG/H
centerC24D472
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC23×C16×C59C2
socle, prime radicalC24×C59D8
hypercenterC23×C16D59
hypocenterC59C23×Q32
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076050);