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3−1+2×C7⋊C8 #13094169

order1512
automorphism?
homologyAbelianization (H1) = C32×C8 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×C7⋊C8

Splittings

HallC7×3−1+2 ⋊ C8
SylowC7 ⋊ C8×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3×C4C32×D7
commutatorC3×C7C32×C8
FittingC4×C7×3−1+2C2
socleC2×C3×C7C32×C4
prime radicalC2×C32×C7C3×C4
cosocleC3×C4×C7C2×C32
hypercenterC4×3−1+2D7
hypocenterC7C8×3−1+2
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C3×C4 ◁ C4×3−1+2

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 504

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,4,3,6,8,7,5,9)(11,12)(13,14)(15,16)(17,18,19,21,20,22,23,24);(2,5,6)(4,8,9)(10,11,13,15,16,14,12)

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 66);