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C52×C7×Dic39 #41031450

order27300
automorphism?
homologyAbelianization (H1) = C4×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52×C7×Dic39
unambiguous semidirect productC3⋊(C52×C7×Dic13)

Splittings

derived, HallC3×C13 ⋊ C4×C52×C7
HallC3×C52×C7×C13 ⋊ C4
HallC52×C7×C13 ⋊ Dic3
HallC3×C52×C13 ⋊ C4×C7
HallC3×C52×C7 ⋊ Dic13
HallC52×C13 ⋊ C7×Dic3
HallC3×C7×C13 ⋊ C4×C52
HallC7×C13 ⋊ C52×Dic3
HallC3×C52 ⋊ C7×Dic13
HallC3×C7 ⋊ C52×Dic13
SylowC13 ⋊ C52×C7×Dic3
SylowC3 ⋊ C52×C7×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C52×C7D39
commutator, hypocenterC3×C13C4×C52×C7
FrattiniC2C52×C7×D39
Fitting, socle, prime radicalC2×C3×C52×C7×C13C2
cosocleC2×C3×C13C2×C52×C7
LCSG ▷ C3×C13
UCSC1 ◁ C2×C52×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 27300

Conjugacy classes & character table

7350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 340);