Finite Group Databasebeta

#39906503

order25952
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC811 ⋊ #106

Subgroups

subgroupG/H
centerC22C22⋊D811
commutatorC4×C811C2×C4
FrattiniC2×C4C2×D811
FittingC4⋊C4×C811C2
socle, prime radicalC22×C811D4
cosocleC2×C4×C811C22
hypercenterC4⋊C4D811
hypocenterC811#106
LCSG ▷ C4×C811 ▷ C2×C811 ▷ C811
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25952

Polycyclic presentation:

2^5,811|a^2=d,b^2=c,c^2=e,b^a=bc,c^a=ce,f^b=f^810

Conjugacy classes & character table

4064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25952, 77);