Finite Group Databasebeta

C4×#16863836 #31009158

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16863836

Splittings

SylowC67 ⋊ C4×#510

Subgroups

subgroupG/H
centerC2×C4C2×#11761613
commutatorC8×C67C23×C4
FrattiniC2×C8C23×D67
FittingC4×#135×C67C2
socleC22×C67C22×D8
prime radicalC2×#135×C67C22
cosocleC2×C8×C67C24
hypercenterC4×#135D67
hypocenterC67C4×#510
LCSG ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 322895);