Finite Group Databasebeta

C2×#22554477 #30682701

order16832
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22554477

Splittings

SylowC263 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D263
commutatorC2×C263C23×C4
FrattiniC4C23×D263
Fitting, prime radicalC2×#41×C263C2
socleC22×C263C22×C4
cosocleC4×C263C24
hypercenterC2×#41D263
hypocenterC263C2×#131
LCSG ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8416

Conjugacy classes & character table

2660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#46782549, #46782550, #46782585, …
maximal normal subgroup of#46782549, #46782550, #46782585, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 1312);