Finite Group Databasebeta

C2×#22558317 #30770753

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22558317

Splittings

SylowC67 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#14523964
commutatorC8×C67C2×C42
FrattiniC22×C8C22×D67
FittingC22×#107×C67C2
socleC23×C67#102
prime radicalC24×C67SD16
cosocleC22×C8×C67C23
hypercenterC22×#107D67
hypocenterC67C2×#1387
LCSG ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#107

614 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, 84490);