Finite Group Databasebeta

C23×#14523977 #31719476

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#14523977

Splittings

SylowC67 ⋊ C23×#107

Subgroups

subgroupG/H
centerC25D268
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC24×C8×C67C2
socle, prime radicalC25×C67D4
cosocleC2×C4×C67C25
hypercenterC24×C8D67
hypocenterC67C23×#107
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C25 ◁ C24×C4 ◁ C24×C8

3614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033213);