Finite Group Databasebeta

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C2×C4⋊C4×C67⋊C8 #30853761

order17152
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×C67⋊C8

Splittings

SylowC67 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC2×C67C22×C4×C8
FrattiniC22×C4C23×D67
FittingC2×C4×C4⋊C4×C67C2
socle, prime radicalC24×C67C22×C4
cosocleC22×C4×C67C24
hypercenterC2×C4×C4⋊C4D67
hypocenterC67C2×C8×C4⋊C4
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 167498);