Finite Group Databasebeta

C23×(C2×D67)⋊C8 #31719257

order17152
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×(C2×D67)⋊C8

Splittings

FittingC24×C8×C67 ⋊ C2
SylowC67 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D67
commutatorC2×C67C24×C8
FrattiniC2×C4C24×D67
FittingC24×C8×C67C2
socleC25×C67C2×C4
prime radicalC25×D67C4
cosocleC2×C4×C67C25
hypercenterC24×C8D67
hypocenterC67C23×C22⋊C8
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C24×C4 ◁ C24×C8

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 1032994);