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C52×C11×Dic21 #37528394

order23100
automorphism?
homologyAbelianization (H1) = C4×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×C11×Dic21
unambiguous semidirect productC3⋊(C52×C11×Dic7)
unambiguous semidirect productC7⋊(C52×C11×Dic3)

Splittings

derived, HallC3×C7 ⋊ C4×C52×C11
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ C4×C11
HallC3×C7×C11 ⋊ C4×C52
HallC52×C7 ⋊ C11×Dic3
HallC7×C11 ⋊ C52×Dic3
HallC3×C52 ⋊ C11×Dic7
HallC3×C11 ⋊ C52×Dic7
SylowC7 ⋊ C52×C11×Dic3
SylowC3 ⋊ C52×C11×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C52×C11D21
commutator, hypocenterC3×C7C4×C52×C11
FrattiniC2C52×C11×D21
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C3×C7C2×C52×C11
LCSG ▷ C3×C7
UCSC1 ◁ C2×C52×C11

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

6600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 205);