Finite Group Databasebeta

C2×#22561743 #30885603

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22561743

Splittings

FittingC2×#384×C67 ⋊ C2
SylowC67 ⋊ C2×#2094

Subgroups

subgroupG/H
centerC24C2×C22⋊D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#384×C67C2
socleC24×C67C2×D4
prime radicalC23×D268C22
hypercenterC2×#384D67
hypocenterC67C2×#2094
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#384

1454 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, 199340);