Finite Group Databasebeta

C2×#22569341 #31720902

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22569341

Splittings

SylowC67 ⋊ C2×#2991

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×C4×#41×C67C2
socleC23×C67C23×C4
prime radicalC22×#41×C67C4
cosocleC2×C4×C67C25
hypercenterC2×C4×#41D67
hypocenterC67C2×#2991
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

2186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1034639);