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C7×C3⋊(C11⋊#1039) #37528387

order23100
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×C3⋊(C11⋊#1039)
unambiguous semidirect productC3⋊(C7×C11⋊#1039)
unambiguous semidirect productC11⋊(C7×C3⋊#1039)

Splittings

derived, HallC3×C52×C11 ⋊ C4×C7
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ #1039
HallC52×C7 ⋊ Dic33
HallC7×C11 ⋊ C3⋊#1039
HallC3×C52 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×#1039
SylowC52 ⋊ C7×Dic33
HallC3×C7 ⋊ C11⋊#1039
SylowC11 ⋊ C7×C3⋊#1039
SylowC3 ⋊ C7×C11⋊#1039

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊D55)
commutator, hypocenterC3×C52×C11C4×C7
FrattiniC2C7×C3⋊(C5⋊D55)
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C3×C52×C11C2×C7
LCSG ▷ C3×C52×C11
UCSC1 ◁ C2×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

5796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 198);