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C11×#14523572 #37528373

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×#14523572

Splittings

derived, HallC52×C7 ⋊ C3×C4×C11
HallC11×C7⋊#1039 ⋊ C3
HallC7×C11×C52⋊C3 ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC11×C52⋊C3 ⋊ Dic7
HallC7⋊#1039 ⋊ C3×C11
HallC7×C52⋊C3 ⋊ C4×C11
HallC52×C11 ⋊ C3×Dic7
HallC7×C11 ⋊ #1039⋊C3
HallC52⋊C3 ⋊ C11×Dic7
SylowC52 ⋊ C3×C11×Dic7
SylowC7 ⋊ C11×#1039⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#11760384
commutator, hypocenterC52×C7C3×C4×C11
FrattiniC2C11×#11760384
Fitting, socleC2×C52×C7×C11C2×C3
prime radicalC2×C7×C11×C52⋊C3C2
cosocleC2×C52×C7C2×C3×C11
LCSG ▷ C52×C7
UCSC1 ◁ C2×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 184);