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C52×C7×Dic33 #37528395

order23100
automorphism?
homologyAbelianization (H1) = C4×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52×C7×Dic33
unambiguous semidirect productC3⋊(C52×C7×Dic11)

Splittings

derived, HallC3×C11 ⋊ C4×C52×C7
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ C4×C7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ C4×C52
HallC7×C11 ⋊ C52×Dic3
HallC3×C52 ⋊ C7×Dic11
HallC3×C7 ⋊ C52×Dic11
SylowC11 ⋊ C52×C7×Dic3
SylowC3 ⋊ C52×C7×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C52×C7D33
commutator, hypocenterC3×C11C4×C52×C7
FrattiniC2C52×C7×D33
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C3×C11C2×C52×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C52×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

6300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 206);