Finite Group Databasebeta

← Prev (#42117408) Next (#42117410) →

C4×C7×#11758281 #42117409

order27468
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×#11758281

Splittings

Fitting, HallC4×C7×C109 ⋊ C9
derived, SylowC109 ⋊ C4×C7×C9
HallC7×C109 ⋊ C4×C9
HallC4×C109 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC4×C7#11758281
commutator, hypocenterC109C4×C7×C9
FrattiniC2C2×C7×#11758281
FittingC4×C7×C109C9
socleC2×C7×C109C2×C9
prime radicalC2×C7×C109⋊C3C2×C3
cosocleC2×C109⋊C3C2×C3×C7
LCSG ▷ C109
UCSC1 ◁ C4×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3052

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27468, 90);