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2−1+4×C7⋊C8 #14219833

order1792
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×C7⋊C8

Splittings

SylowC7 ⋊ C8×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D7
commutatorC2×C7C24×C8
FittingC4×C7×2−1+4C2
socleC22×C7C24×C4
prime radicalC2×C7×2−1+4C4
cosocleC2×C4×C7C25
hypercenterC4×2−1+4D7
hypocenterC7C8×2−1+4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1035605);