Finite Group Databasebeta

← Prev (#37558851) Next (#37558853) →

C11⋊C5×D217 #37558852

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

Aliases

direct productC11⋊C5×D217
unambiguous semidirect productC7⋊(C11⋊C5×D31)

Splittings

Fitting, socle, derived, HallC7×C11×C31 ⋊ C2×C5
HallC7×C31×C11⋊C5 ⋊ C2
HallC11×D217 ⋊ C5
HallC31×C11⋊C5 ⋊ D7
HallC7×C11⋊C5 ⋊ D31
HallC11×C31 ⋊ C5×D7
HallC7×C31 ⋊ C2×C11⋊C5
HallC7×C11 ⋊ C5×D31
SylowC31 ⋊ D7×C11⋊C5
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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23870, 48);