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C37⋊C3×C7⋊AGL(1,𝔽5) #29509591

order15540
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC37⋊C3×C7⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C7×C37 ⋊ C3×C4
HallC37×C7⋊AGL(1,𝔽5) ⋊ C3
HallC5×C7×C37⋊C3 ⋊ C4
HallC7×C37⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C37⋊C3 ⋊ Dic7
HallC7×C37 ⋊ C3×AGL(1,𝔽5)
HallC5×C37 ⋊ C3×Dic7
SylowC37 ⋊ C3×C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ C4×C37⋊C3
SylowC7 ⋊ AGL(1,𝔽5)×C37⋊C3
SylowC5 ⋊ Dic7×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C37C3×C4
prime radicalC7×D5×C37⋊C3C2
cosocleC7×D5×C37C2×C3
LCSG ▷ C5×C7×C37
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 93);