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C7×C11⋊#64480 #37528484

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

Aliases

direct productC7×C11⋊#64480
unambiguous semidirect productC11⋊(C7×#64480)

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ Dic3
derived, HallC11×C52⋊C3 ⋊ C4×C7
HallC7×C11×C52⋊C3 ⋊ C4
HallC7×C52⋊C3 ⋊ Dic11
HallC52×C11 ⋊ C7×Dic3
HallC52×C7 ⋊ Dic33
HallC7×C11 ⋊ #64480
HallC52⋊C3 ⋊ C7×Dic11
SylowC52 ⋊ C7×Dic33
SylowC11 ⋊ C7×#64480

Subgroups

subgroupG/H
center, hypercenterC7C11⋊#64480
commutator, hypocenterC11×C52⋊C3C4×C7
FrattiniC1G
Fitting, socleC52×C7×C11Dic3
prime radicalC7×C11×(C5⋊D5)⋊C3C2
cosocleC11×(C5⋊D5)⋊C3C2×C7
LCSG ▷ C11×C52⋊C3
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 295);