Finite Group Databasebeta

C4×(C2×D67)⋊C16 #30770859

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

Aliases

direct productC4×(C2×D67)⋊C16

Splittings

FittingC2×C4×C16×C67 ⋊ C2
SylowC67 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
centerC2×C4×C8C2×D67
commutatorC2×C67C2×C4×C16
FrattiniC22×C8C22×D67
FittingC2×C4×C16×C67C2
socleC23×C67C22×C8
prime radicalC23×D67C2×C8
cosocleC22×C8×C67C23
hypercenterC2×C4×C16D67
hypocenterC67C4×C22⋊C16
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

614 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, 84596);