Finite Group Databasebeta

C4×C4⋊C8×D67 #30853700

order17152
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C4⋊C8×D67

Splittings

FittingC4×C4⋊C8×C67 ⋊ C2
SylowC67 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22×D67
commutatorC2×C67C22×C4×C8
FrattiniC22×C4C23×D67
FittingC4×C4⋊C8×C67C2
socleC23×C67C23×C4
prime radicalC23×D67C22×C4
cosocleC22×C4×C67C24
hypercenterC4×C4⋊C8D67
hypocenterC67C2×C4×C4⋊C8
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1550 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, 167437);