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C52×C3⋊(C7⋊#261) #41031963

order27300
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×C3⋊(C7⋊#261)
unambiguous semidirect productC3⋊(C52×C7⋊#261)
unambiguous semidirect productC7⋊(C52×C3⋊#261)

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C4
derived, HallC3×C7×C13 ⋊ C4×C52
HallC52×C7×C13 ⋊ Dic3
HallC3×C52×C13 ⋊ Dic7
HallC3×C52×C7 ⋊ #261
HallC52×C13 ⋊ Dic21
HallC52×C7 ⋊ C3⋊#261
HallC7×C13 ⋊ C52×Dic3
HallC3×C52 ⋊ C7⋊#261
HallC3×C13 ⋊ C52×Dic7
HallC3×C7 ⋊ C52×#261
SylowC13 ⋊ C52×Dic21
SylowC7 ⋊ C52×C3⋊#261
SylowC3 ⋊ C52×C7⋊#261

Subgroups

subgroupG/H
center, hypercenterC52C3⋊(C7⋊#261)
commutator, hypocenterC3×C7×C13C4×C52
FrattiniC1G
Fitting, socleC3×C52×C7×C13C4
prime radicalC3×C52×C7×D13C2
cosocleC3×C7×D13C2×C52
LCSG ▷ C3×C7×C13
UCSC1 ◁ C52

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6825

Conjugacy classes & character table

2175 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 853);