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C5×C11⋊C5×Dic21 #37528347

order23100
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×Dic21
unambiguous semidirect productC3⋊(C5×Dic7×C11⋊C5)
unambiguous semidirect productC7⋊(C5×Dic3×C11⋊C5)
unambiguous semidirect product(C11×Dic21)⋊C52
unambiguous semidirect product(C5×C11×Dic21)⋊C5

Splittings

derived, HallC3×C7×C11 ⋊ C4×C52
HallC3×C5×C7×C11⋊C5 ⋊ C4
HallC5×C7×C11⋊C5 ⋊ Dic3
HallC11×Dic21 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ Dic7
HallC7×C11 ⋊ C52×Dic3
HallC3×C11 ⋊ C52×Dic7
HallC3×C7 ⋊ C4×C5×C11⋊C5
SylowC11 ⋊ C52×Dic21
SylowC7 ⋊ C5×Dic3×C11⋊C5
SylowC3 ⋊ C5×Dic7×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D21×C11⋊C5
commutator, hypocenterC3×C7×C11C4×C52
FrattiniC2C5×D21×C11⋊C5
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C3×C7×C11C2×C52
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 158);