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C7⋊((C11⋊C5)⋊D31) #37558864

order23870
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC7⋊((C11⋊C5)⋊D31)
unambiguous semidirect product(C11⋊C5)⋊D217

Splittings

Fitting, socle, derived, HallC7×C11×C31 ⋊ C2×C5
HallC7×C31×C11⋊C5 ⋊ C2
HallD2387 ⋊ C5
HallC31×C11⋊C5 ⋊ D7
HallC7×C11⋊C5 ⋊ D31
HallC11×C31 ⋊ C5×D7
HallC7×C31 ⋊ AGL(1,𝔽11)
HallC7×C11 ⋊ C5×D31
HallC11⋊C5 ⋊ D217
SylowC31 ⋊ C7⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×D217
SylowC7 ⋊ (C11⋊C5)⋊D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C31C2×C5
LCSG ▷ C7×C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Polycyclic presentation:

2,5,7,11,31|c^a=c^6,d^a=d^10,e^a=e^30,d^b=d^4

Conjugacy classes & character table

767 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 60);