Finite Group Databasebeta

C22×(C2×D67)⋊C16 #31008495

order17152
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D67)⋊C16

Splittings

FittingC23×C16×C67 ⋊ C2
SylowC67 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D67
commutatorC2×C67C23×C16
FrattiniC2×C8C23×D67
FittingC23×C16×C67C2
socleC24×C67C2×C8
prime radicalC24×D67C8
cosocleC2×C8×C67C24
hypercenterC23×C16D67
hypocenterC67C22×C22⋊C16
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C8 ◁ C23×C16

1470 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, 322232);