Finite Group Databasebeta

C2×#22558047 #30745324

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22558047

Splittings

SylowC67 ⋊ C2×#1278

Subgroups

subgroupG/H
centerC2×C42C22⋊D67
commutatorC4×C67C2×C4×C8
FrattiniC2×C42C22×D67
FittingC2×C4×M16×C67C2
socleC23×C67#95
prime radicalC24×C67C4⋊C4
cosocleC2×C42×C67C23
hypercenterC2×C4×M16D67
hypocenterC67C2×#1278
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×M16

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59061);