Finite Group Databasebeta

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C32×Dic113⋊C7 #43249803

order28476
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×Dic113⋊C7
unambiguous semidirect productDic113⋊(C32×C7)
unambiguous semidirect product(C3×Dic113)⋊(C3×C7)
unambiguous semidirect product(C32×Dic113)⋊C7

Splittings

derived, SylowC113 ⋊ C32×C4×C7
HallC32×C113⋊C7 ⋊ C4
HallC32×Dic113 ⋊ C7
HallC32×C113 ⋊ C4×C7
HallC113⋊C7 ⋊ C32×C4
HallDic113 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32D113⋊C7
commutator, hypocenterC113C32×C4×C7
FrattiniC2C32×D113⋊C7
Fitting, socleC2×C32×C113C2×C7
prime radicalC2×C32×C113⋊C7C2
cosocleC2×C113C2×C32×C7
LCSG ▷ C113
UCSC1 ◁ C2×C32

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4068

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28476, 54);