Finite Group Databasebeta

C23×#14523953 #31719213

order17152
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210

Aliases

direct productC23×#14523953

Splittings

SylowC67 ⋊ C23×#97

Subgroups

subgroupG/H
centerC24×C4C2×D67
commutatorC2×C67C23×C42
FrattiniC2×C4C24×D67
FittingC24×C8×C67C2
socle, prime radicalC25×C67C2×C4
cosocleC2×C4×C67C25
hypercenterC24×C8D67
hypocenterC67C23×#97
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C24×C4 ◁ C24×C8

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

4384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1032950);