Finite Group Databasebeta

C2×#22558100 #30745992

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

Aliases

direct productC2×#22558100

Splittings

SylowC67 ⋊ C2×#1299

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC2×#431×C67C2
socleC23×C67#95
prime radicalC24×C67C4⋊C4
cosocleC2×C42×C67C23
hypercenterC2×#431D67
hypocenterC67C2×#1299
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59729);