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C2×C7×D127⋊C7 #38733533

order24892
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C7×D127⋊C7
unambiguous semidirect productD127⋊(C2×C72)
unambiguous semidirect product(C2×D127)⋊C72
unambiguous semidirect product(C127⋊C7)⋊(C22×C7)
unambiguous semidirect product(C2×C127⋊C7)⋊(C2×C7)
unambiguous semidirect product(C2×C7×D127)⋊C7

Splittings

Fitting, socleC2×C7×C127 ⋊ C2×C7
derived, SylowC127 ⋊ C22×C72
HallC7×C127⋊C7 ⋊ C22
HallC2×D127 ⋊ C72

Subgroups

subgroupG/H
center, hypercenterC2×C7D127⋊C7
commutator, cosocle, hypocenterC127C22×C72
FrattiniC1G
Fitting, socleC2×C7×C127C2×C7
LCSG ▷ C127
UCSC1 ◁ C2×C7

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1778

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24892, 26);