Finite Group Databasebeta

C2×#22558067 #30745606

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#22558067

Splittings

SylowC67 ⋊ C2×#1286

Subgroups

subgroupG/H
centerC23C67⋊#95
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC2×#382×C67C2
socleC23×C67#95
prime radicalC24×C67C22⋊C4
cosocleC2×C42×C67C23
hypercenterC2×#382D67
hypocenterC67C2×#1286
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 59343);