Finite Group Databasebeta

C2×C4×#14523964 #30853569

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#14523964

Splittings

SylowC67 ⋊ C2×C4×#102

Subgroups

subgroupG/H
centerC23×C4C22⋊D67
commutatorC4×C67C22×C42
FrattiniC22×C4C23×D67
FittingC22×C4×D4×C67C2
socleC24×C67C2×D4
prime radicalC23×D4×C67C22
cosocleC22×C4×C67C24
hypercenterC22×C4×D4D67
hypocenterC67C2×C4×#102
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×D4

2158 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, 167306);