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C23×C7⋊(C11⋊AGL(1,𝔽5)) #47978447

order35420
automorphism?
homologyAbelianization (H1) = C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C7⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C23×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C23×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C4
derived, HallC5×C7×C11 ⋊ C4×C23
HallC7×C11×C23 ⋊ AGL(1,𝔽5)
HallC5×C11×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ Dic11
HallC11×C23 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C23 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C23 ⋊ Dic77
HallC7×C11 ⋊ AGL(1,𝔽5)×C23
HallC5×C11 ⋊ C23×Dic7
HallC5×C7 ⋊ C23×Dic11
SylowC11 ⋊ C23×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C23×C11⋊AGL(1,𝔽5)
SylowC5 ⋊ C23×Dic77

Subgroups

subgroupG/H
center, hypercenterC23C7⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C11C4×C23
FrattiniC1G
Fitting, socleC5×C7×C11×C23C4
prime radicalC7×D5×C11×C23C2
cosocleC7×D5×C11C2×C23
LCSG ▷ C5×C7×C11
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

3611 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 81);