Finite Group Databasebeta

C22⋊C4×C67⋊C16 #30770912

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×C67⋊C16

Splittings

SylowC67 ⋊ C16×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D67
commutatorC2×C67C2×C4×C16
FittingC8×C22⋊C4×C67C2
socleC23×C67C22×C8
prime radicalC24×C67C2×C8
cosocleC22×C8×C67C23
hypercenterC8×C22⋊C4D67
hypocenterC67C16×C22⋊C4
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C8 ◁ C8×C22⋊C4

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 84649);