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C7×#16839052 #41031376

order27300
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×#16839052

Splittings

derived, HallC52×C13 ⋊ C3×C4×C7
HallC7×#13049918 ⋊ C3
HallC52×C7×C13⋊C3 ⋊ C4
HallC52×C7×C13 ⋊ C3×C4
Hall#13049918 ⋊ C3×C7
HallC52×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ #1039
HallC52×C7 ⋊ Dic13⋊C3
HallC7×C13 ⋊ C3×#1039
HallC13⋊C3 ⋊ C7×#1039
SylowC52 ⋊ C7×Dic13⋊C3
SylowC13 ⋊ C3×C7×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊(C5⋊(D13⋊C3))
commutator, hypocenterC52×C13C3×C4×C7
FrattiniC2C7×C5⋊(C5⋊(D13⋊C3))
Fitting, socleC2×C52×C7×C13C2×C3
prime radicalC2×C52×C7×C13⋊C3C2
cosocleC2×C52×C13C2×C3×C7
LCSG ▷ C52×C13
UCSC1 ◁ C2×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 266);